全相位FIR滤波器组
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摘要
首先,本文基于全相位DFT数字滤波器的直接频域实现网络结构,对输入或输出数据加窗,导出了一种新型的加窗全相位DFT数字滤波器。它的频率特性比不加窗又有很大提高,幅频响应等于或逼近频率采样值,通带纹波极小,阻带衰减极大,过渡带陡峭,零相位,滤波性能和实现的简洁性超过其他传统方法。它除了可以采用通常的卷积结构外,也可以采用直接频域网络实现,本文给出了它的直接频域网络组成及其简化算法。这种网络具有实时自设计功能,可构成时变系统用于滤波器传递函数实时可变的场合,便于集成为频响和长度均可编程的通用零相位数字滤波器,是数字滤波器的一种新的设计理念和实现结构。
其次,本文提出一种新型的半带滤波器—全相位半带滤波器(APHF),这种半带滤波器具有频率采样特性,通带和阻带纹波小,过渡带陡峭,频率响应没有过冲,可以直接进行谱分解用于设计二通道完全重建正交镜像滤波器(QMF)组。本文针对这种半带波器提出了新的高精度谱分解方法。与传统半带滤波器谱分解设计二通道完全重建QMF组相比,QMF组的重建精度由10?3dB提高到10?6dB,是半带滤波器和准确重建二通道QMF组的一种新的设计方法。
最后,本文把加窗全相位DFT数字滤波器的设计方法用于设计具有上述优点的全相位M带滤波器,从而得到全相位均匀滤波器组。全相位均匀滤波器组可以用于时频分析—加窗傅里叶变换。小波变换是时频分析的有力工具,但不适合线性charp信号的分析。加窗全相位可以有效减小窗函数的旁瓣,特别适用于线性charp信号的时频分析。
First, based on the architecture of the APDFT filter, this paper brings out a newtype of zero-phase digital filter called the windowed all phase DFT (WAPDFT)digital filter, by windowing the input and/or output data of the DFT/IDFT blocks inthe APDFT filter network. The frequency characteristics of the APDFT filter areimproved greatly by this way. While the frequency response of the filter still passes orapproaches the desired frequency samples, it has much less pass-band and stop-bandripples, and sharp transition. The WAPDFT filter can be implemented with commonconvolution structure and the frequency domain direct network like the APDFT filter,and realized in a simplified structure also. This paper gives the network of the newstructure and the associate algorithm. This network is not sensitive to finite wordlength effect compared with traditional frequency sampling structures. It has real-timeself-design function and may constitute a time-variant system. It can be easilyintegrated into a universal zero-phase digital filter with frequency response and lengthprogrammable.
Second, this paper proposes a new type of half band filter—the all phase halfband filter (APHF). It has the property of frequency sampling, i.e. the response curvepasses desired frequency samples. Its frequency response has very small pass-bandripple, great stop-band attenuation, sharp transition band and without overshootingwhether in stop-band or pass-band. It can be used to design two-channel perfectreconstruction QMF (quadrature mirror filter) banks by factorizing the spectrum forthe APHF directly. A new method is given to get the spectral factors of the APHFwith high precision. Compared with traditional spectral factorization method ofdesigning two-channel perfect reconstruction QMF banks, the QMF banks designedby factorizing APHF has better reconstruction precision that the error is decreasedfrom 10?3dB to10?6dB. It's a new method for designing half band filters andtwo-channel perfect reconstruction QMF banks.
Finally, using the WAPDFT filter design method, this paper proposes an allphase M band filter with all the advantages mentioned above and an all phase uniformDFT filter bank. The uniform DFT filter bank can be used to time-frequencyanalysis—windowed fourier transform. Although wavelet transform is a useful toolfor time-frequency analysis, it is not suitable for analysing linear charp signals.
Whereas, the all phase uniform DFT filter bank can do it very well duo to thewindowed all phase can efficiently reduce the side lobes of the window.
其次,本文提出一种新型的半带滤波器—全相位半带滤波器(APHF),这种半带滤波器具有频率采样特性,通带和阻带纹波小,过渡带陡峭,频率响应没有过冲,可以直接进行谱分解用于设计二通道完全重建正交镜像滤波器(QMF)组。本文针对这种半带波器提出了新的高精度谱分解方法。与传统半带滤波器谱分解设计二通道完全重建QMF组相比,QMF组的重建精度由10?3dB提高到10?6dB,是半带滤波器和准确重建二通道QMF组的一种新的设计方法。
最后,本文把加窗全相位DFT数字滤波器的设计方法用于设计具有上述优点的全相位M带滤波器,从而得到全相位均匀滤波器组。全相位均匀滤波器组可以用于时频分析—加窗傅里叶变换。小波变换是时频分析的有力工具,但不适合线性charp信号的分析。加窗全相位可以有效减小窗函数的旁瓣,特别适用于线性charp信号的时频分析。
First, based on the architecture of the APDFT filter, this paper brings out a newtype of zero-phase digital filter called the windowed all phase DFT (WAPDFT)digital filter, by windowing the input and/or output data of the DFT/IDFT blocks inthe APDFT filter network. The frequency characteristics of the APDFT filter areimproved greatly by this way. While the frequency response of the filter still passes orapproaches the desired frequency samples, it has much less pass-band and stop-bandripples, and sharp transition. The WAPDFT filter can be implemented with commonconvolution structure and the frequency domain direct network like the APDFT filter,and realized in a simplified structure also. This paper gives the network of the newstructure and the associate algorithm. This network is not sensitive to finite wordlength effect compared with traditional frequency sampling structures. It has real-timeself-design function and may constitute a time-variant system. It can be easilyintegrated into a universal zero-phase digital filter with frequency response and lengthprogrammable.
Second, this paper proposes a new type of half band filter—the all phase halfband filter (APHF). It has the property of frequency sampling, i.e. the response curvepasses desired frequency samples. Its frequency response has very small pass-bandripple, great stop-band attenuation, sharp transition band and without overshootingwhether in stop-band or pass-band. It can be used to design two-channel perfectreconstruction QMF (quadrature mirror filter) banks by factorizing the spectrum forthe APHF directly. A new method is given to get the spectral factors of the APHFwith high precision. Compared with traditional spectral factorization method ofdesigning two-channel perfect reconstruction QMF banks, the QMF banks designedby factorizing APHF has better reconstruction precision that the error is decreasedfrom 10?3dB to10?6dB. It's a new method for designing half band filters andtwo-channel perfect reconstruction QMF banks.
Finally, using the WAPDFT filter design method, this paper proposes an allphase M band filter with all the advantages mentioned above and an all phase uniformDFT filter bank. The uniform DFT filter bank can be used to time-frequencyanalysis—windowed fourier transform. Although wavelet transform is a useful toolfor time-frequency analysis, it is not suitable for analysing linear charp signals.
Whereas, the all phase uniform DFT filter bank can do it very well duo to thewindowed all phase can efficiently reduce the side lobes of the window.
引文
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